A variation of the Ito theorem

作者：Morigi Marta; Shumyatsky Pavel^*

来源：Journal of Algebra, 2010, 324(8): 2052-2057.

DOI：10.1016/j.jalgebra.2010.07.016

• Products of groups
• Metabelian groups

Let X be a normal subset of a group G such that X subset of AB for some abelian subgroups A and B. Our main result is that X generates a metabelian subgroup (Theorem 1.1). In the case where X = G this is well-known Ito's theorem. From this we deduce that if G is finite and A and B are pi-subgroups, then X generates a pi-subgroup (Theorem 1.2). We also show that if G is finite and e is a prime-power such that A and B have exponents dividing e, then the exponent of < X > is e-bounded (Theorem 1.3).

• 出版日期2010-10-15